Question: Given $ m \angle ABC = 2x + 125$, and $ m \angle CBD = 3x + 10$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Answer: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {2x + 125} + {3x + 10} = {180}$ Combine like terms: $ 5x + 135 = 180$ Subtract $135$ from both sides: $ 5x = 45$ Divide both sides by $5$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 2({9}) + 125$ Simplify: $ {m\angle ABC = 18 + 125}$ So ${m\angle ABC = 143}$.